working from right to left. To add the VII, put another counter between the X and I lines and two more counters on the I line. The I line now has six counters on it. We remove five of them and put instead another counter between the X and I lines. Of the three counters now between the X and I lines we "carry over" two of them as a sing counter on the X line. We now add the XXX by putting three more counters on the X line. Since we now have a total of five counters on the X line they are replaced by a single counter between the C and X line, and the two counters now found there are "carried over " as a single counter on the C line. We finally add the M by putting another counter on the M line. The final appearance of our frame is illustrated at the right in Figure 1 and the sum can be read off as MMDCCCVI. We have obtained the sum of the two numbers by simple mechanical operations and without requiring any scratch paper.